Consider the following ANOVA experiments. (Give your answers correct to two decimal places.)
(b) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05.
F .
(c) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05.
F
To determine the critical region and critical value for an ANOVA test, you need to use the F-distribution table.
(b) For the null hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05, you can find the critical value by following these steps:
1. Determine the degrees of freedom for the numerator: df1 = k - 1 = 5 - 1 = 4, where k is the number of groups (levels).
2. Determine the degrees of freedom for the denominator: df2 = N - k = 17 - 5 = 12, where N is the total number of observations.
3. Look up the critical F-value in the F-distribution table with an alpha level (á) of 0.05, degrees of freedom df1 = 4, and df2 = 12. Find the value that corresponds to the intersection of these values. Let's call this critical value F*.
4. The critical region is defined by F > F*, where F is the calculated F-statistic from your data. If the calculated F-statistic falls in the critical region, you would reject the null hypothesis.
(c) For the null hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05, you can follow the same steps as in (b):
1. Determine the degrees of freedom for the numerator: df1 = k - 1 = 3 - 1 = 2, where k is the number of groups (levels).
2. Determine the degrees of freedom for the denominator: df2 = N - k = 19 - 3 = 16, where N is the total number of observations.
3. Look up the critical F-value in the F-distribution table with an alpha level (á) of 0.05, degrees of freedom df1 = 2, and df2 = 16. Find the value that corresponds to the intersection of these values. Let's call this critical value F*.
4. The critical region is defined by F > F*, where F is the calculated F-statistic from your data. If the calculated F-statistic falls in the critical region, you would reject the null hypothesis.
Please note that the F-distribution table can be found in most statistical textbooks or online. You need to locate the appropriate row (numerator degrees of freedom) and column (denominator degrees of freedom) to find the critical value.